Question

Pam and Rachel buy books at the bookstore where Rachel works. Each uses a coupon. As an employee Rachel pays only 75% of the advertised price after her coupon is applied. Pam bought books for $4.00 each and used a $5.00 off coupon. Rachel bought books for $8.00 each and used a $4.00 off coupon. Is it possible for Pam and Rachel to purchase x books and pay the same amount? Use the equation 4x - 5 to represent Pams purchase and 0.75(8x - 4) to represent Rachel's purchase.

Answer 1

The equation 4x - 5 represents Pam's purchase

The equation 0.75(8x - 4) represents Rachel's purchase

If they paid the same,

4x - 5 = 0.75(8x - 4)

4x - 5 = 0.75(8x) - 0.75(4) distributing

4x - 5 = 6x - 3

4x - 5 - 4x= 6x - 3 - 4x subtracting 4x at both sides

-5 = 2x - 3

-5 +3 = 2x - 3 + 3 adding 3 at both sides

-2 = 2x

-2/2 = 2x/2 dividing by 2 at both sides

-1 = x

Given that they can't purchase a negative amount of books, then is not possible that they pay the same amount